*HWDILGJHWVSLQQHU6SLQLW ,QHHGHGWRVSLQ WLPHVWRILQLVK
)LQGWKH*&)XVLQJWKH%LUWKGD\&DNHPHWKRG
*&)
*&)
*&)
*&)
*&)
*&)
*&)
*&)
*&)
*&)
6SLQDJDLQ ,QHHGHGWRVSLQ WLPHVWRILQLVK
)LQGWKH*&)XVLQJWKH%LUWKGD\&DNHPHWKRG
*&) [
*&)
*&)
*&)
*&)
*&)
*&)
*&)
:ULWHHDFKDVDGHFLPDO
KXQGUHGWKVDVDGHFLPDOLV
DVDGHFLPDOLV
DVDGHFLPDOLV
DVDGHFLPDOLV
5RXQGWRWKHQHDUHVW
WKRXVDQG +RZPDQ\PLQXWHVLVLW
IURPDPWRDP" :ULWHWKHPLVVLQJIDPLO\
IDFW
[
¶
¶
,WZDVGHJUHHVEHORZ
]HURLQWKHPRUQLQJ%\
DIWHUQRRQWKHWHPSHUDWXUH
URVHGHJUHHV+RZ
ZDUPZDVLW"
7KHUDGLXVRIDFLUFOHLV
FP:KDWLVWKHGLDPHWHU
RIWKLVFLUFOH"
:KDWLVRI"
[ NP P ¶
,QHDFKJURXSFLUFOHWKHQXPEHUWKDWKDVWKHJUHDWHVWYDOXHDQGSXWDVTXDUHDURXQG
WKHQXPEHUWKDWKDVWKHOHDVWYDOXH
\ :KDWLVWKHOHDVWFRPPRQ
PXOWLSOHRIDQG" :KDWLVWKHOHDVWFRPPRQ
PXOWLSOHRIDQG"
:KDWFRLQVDGGXSWR
FHQWV" ,WZDVGHJUHHVRXWVLGH
:KDWZRXOGWKH
WHPSHUDWXUHEHLILWJRW
GHJUHHVFROGHU"
5RXQGWRWKH
QHDUHVWKXQGUHG
$QQDUROOVDGLH:KDWLVWKH
FKDQFHRIKHUUROOLQJD" NJ J
NJ J ¶
7KH'UHVVHG8S3HW
3DUDGHEHJDQDW
SP7KHSDUDGHZDV
RYHUILIW\PLQXWHVODWHU
:KDWWLPHGLGWKH
SDUDGHHQG"
+ROO\ZDONHGWRWKH
VWRUHLQPLQXWHV6KH
ERXJKW%DQG$LGVIRU
JDX]HIRU
DQGVXQWDQORWLRQIRU
6KHJDYHWKH
FOHUNDELOO6KHOHIW
WKHVWRUHDWDP,W
WRRNKHUPLQXWHVWR
ZDONKRPH+RZPXFK
ORQJHUGLGLWWDNHKHUWR
ZDONKRPHWKDQLWWRRN
WRZDONWRWKHVWRUH"
0LVV:DONHULVJRLQJWR
VL[0DUGL*UDVSDUWLHV
6KHERXJKWDGLIIHUHQW
IHDWKHUPDVNIRUHDFK
SDUW\7KHFRVWVZHUH
DQG:KDW
LVWKHDYHUDJHFRVWRI
WKHPDVNV"
+RZPDQ\GLPHVPDNH" 5HZULWHWKHVHLQLQFUHDVLQJRUGHURIOHQJWK
PNPGPPPFP
&DQEHHYHQO\GLYLGHGE\"&LUFOH
LVHYHQO\GLYLVLEOHE\
LV127HYHQO\GLYLVLEOHE\
&DQ\RXGUDZ21(OLQHJRLQJWKURXJK$//WKHFLUFOHV"<RXUOLQHFDQJROHIWULJKW
XSRUGRZQ,WFDQQRWJRGLDJRQDOO\<RXUOLQHFDQQRWFURVVRYHUDQ\SDUWRI
WKHOLQH\RXKDYHDOUHDG\GUDZQ
<RX08677851LQD%/$&.FLUFOH'R1277851LQD:+,7(FLUFOH
7KHSX]]OHRQWKHOHIWVKRZVDFRUUHFWOLQHJRLQJWKURXJKDOOWKHFLUFOHV
)LQLVKWKHOLQH )LQLVKWKHOLQH
:ULWHLQZRUGV
¶
+RZPDQ\FHQWLPHWHUVDUHLQPLOOLPHWHUV"
FHQWLPHWHUV
6L[VHYHQWKVRIWKHFKLOGUHQLQ
5RELQVRQVFODVVZDQWWRJRRXWVLGH
,I5RELQVRQDJUHHVZLWKWKH
PDMRULW\ZLOOWKHFODVVVWD\LQVLGH
RUJRRXWVLGH"
&LUFOHWKHJUHDWHVWQXPEHU
¶ [
¶
8VHWKHSLHFHVDERYHWRKHOS\RXILOOLQWKHUXQDZD\PDWKSX]]OH
[
)RUZULWHWKHGLJLW
WKDWLVLQWKHKXQGUHG
WKRXVDQGVSODFH ¶
&LUFOHWKHGLJLWLQWKHWHQWKVSODFH
[ [
[ [ ¶
9 x 4 = 6
+
3 9 x 0 = 0 3
6 + =
0 3 2 ÷ = 6
9 8 x 6 = 4 +
= 5 0
4 ÷ 6 = 8 3 x 8 = 2
x 0 3 7 +
9 = 5
= 9 = 0 =
7 6 5
2 5 + 0 = 7 7
1 -
5
[ [ [
8VHWKHSLHFHVDERYHWRKHOS\RXILOOLQWKHUXQDZD\PDWKSX]]OH
:ULWHDQHTXDWLRQWRUHSUHVHQWWKLV
7KHVXPRIHLJKWDQGHOHYHQLVQLQHWHHQ [ [
3
6 = 3 0
5 x 9
= 7 2 x
1 x 3 = 3 4 9
5 8 3 5 ÷ 5 7
0 1 ÷ 2 = 4 8
2 x = 1
7 2 ÷ 8 = 9 2 x 3 =
x 1 = 3 =
8 0 1 x 0 = 0
÷ ÷ 4 ÷
4 6 x 1 = 6 7
= = ÷ 5 6 ÷ 8 = 7
8 3 1 0
= =
4 8 ÷ = 8
7KHUHDUHILYHREMHFWVDZKLWHREMHFWDQDY\REMHFWDSLQNREMHFWD\HOORZREMHFWDQGD
SXUSOHREMHFW(DFKREMHFWKDVDGLIIHUHQWPDVVJJJJDQGJDQG
DGLIIHUHQWYROXPHFXELFFPFXELFFPFXELFFPFXELFFPDQG
FXELFFP
'HQVLW\ 0DVV9ROXPH
)LJXUHRXWWKHPDVVYROXPHDQGGHQVLW\RIHDFKREMHFW
7KHYROXPHRIWKHZKLWHREMHFWLVQRWFXELFFPDQGLWLVDOVRQRWFXELFFP
7KHGHQVLW\RIZDWHULVJUDPVSHUFXELFFP,IWKHSLQNREMHFWZDVSODFHGLQZDWHU
LWZRXOGVLQN
7KH\HOORZREMHFWKDVDYROXPHRIFXELFFPDQGDPDVVRIJ
7KHGHQVLW\RIDOXPLQXPLVJUDPVSHUFXELFFP7KHSXUSOHREMHFWLVPRUHGHQVH
WKDQDOXPLQXP
7KHZKLWHREMHFWKDVDJUHDWHUPDVVWKDQWKHSLQNREMHFW
7KHZKLWHREMHFWKDVDGHQVLW\RIJUDPVSHUFXELFFPDQGDPDVVRIJ
7KHQDY\REMHFWKDVDGHQVLW\RIJUDPVSHUFXELFFPDQGDPDVVRIJ
2QHREMHFWKDVDYROXPHRIFXELFFPDQGDGHQVLW\RIJUDPVSHUFXELFFP
7KHYROXPHRIWKHQDY\REMHFWLVQRWFXELFFPDQGLWLVDOVRQRWFXELFFP
7KHGHQVLW\RIZDWHULVJUDPVSHUFXELFFP,IWKHQDY\REMHFWZDVSODFHGLQZDWHU
LWZRXOGIORDW
ZKLWHREMHFWKDVDPDVVRI DYROXPHRI DQGDGHQVLW\RI QDY\REMHFWKDVDPDVVRI DYROXPHRI DQGDGHQVLW\RI SLQNREMHFWKDVDPDVVRI DYROXPHRI DQGDGHQVLW\RI
\HOORZREMHFWKDVDPDVVRI DYROXPHRI DQGDGHQVLW\RI SXUSOHREMHFWKDVDPDVVRI DYROXPHRI DQGDGHQVLW\RI
[ ¶
-HVVLFDDQG:HQG\HDFKKDYHDVRFFHUJDPHDWDPRQGLIIHUHQWILHOGV-HVVLFDV
VRFFHUILHOGLV\DUGVORQJ:HQG\VVRFFHUILHOGLVIHHWORQJ:KLFKILHOGLVORQJHU
DQGE\KRZPXFK"
,DPDGLJLWQXPEHUWKDWLVGLYLVLEOHE\DQG,I\RXDGGP\GLJLWVWRJHWKHUWKHVXPLV
:KDWQXPEHUDP,"
$GDPWRRNDELJERZOIURPWKHNLWFKHQWRVHHZKDWNLQGRIIXQSDUW\PL[KHFRXOGFUHDWH
+HDGGHG FXSVRI&KHHULRV FXSVRIUDLVLQV FXSVRI*ROGILVKFUDFNHUVDQG
FXSRISUHW]HOV+RZPXFKIRRGLVQRZLQWKHERZO"
,IF DQGW WKHQ
ZKDWLVF
[W
"
¶¶
[[[[
[:KDWLVWKHYDOXHRI["
$SULOFOLPEHGPHWHUVLQ
RQO\VHFRQGV+RZ
PDQ\PHWHUVGLGVKHFOLPE
SHUVHFRQG"
$FLUFOHJUDSKKDVILYH
VHFWLRQV2QO\IRXU
VHFWLRQVDUHODEHOHG7KH
ODEHOVDUH
DQG:KDWVKRXOGWKH
PLVVLQJVHFWLRQEH"
5HZULWHDVDQDOJHEUDLF
H[SUHVVLRQRUHTXDWLRQ
$GGGWRWKHSURGXFWRI
DQG
)LOOLQWKHPLVVLQJQXPEHUV
2QO\UXOH7KHVDPHQXPEHU&$1127EHQH[WWRHDFKRWKHULQ$1<GLUHFWLRQ
'DUNOLQHVVXUURXQGDEORFN1XPEHUVWRXVHLQDEORFN
$EORFNZLWKVSDFHKDVWREHWKHQXPEHU
$EORFNZLWKVSDFHVPXVWKDYHWKHQXPEHUVDQG
$EORFNZLWKVSDFHVPXVWKDYHWKHQXPEHUVDQG
$EORFNZLWKVSDFHVPXVWKDYHWKHQXPEHUVDQG
$QHQWLUHEORFNZLWKVSDFHVLVEODQN6LQFH WKHEORFNLVVSDFHVLWXVHVWKHQXPEHUV
$QHQWLUHEORFNZLWKVSDFHVLVEODQN6LQFH WKHEORFNLVVSDFHVLWXVHVWKHQXPEHUV
+LQW7KHVHQXPEHUVDUHPLVVLQJ
+LQW7KHVHQXPEHUVDUHPLVVLQJ
(DFKURZFROXPQDQGER[PXVWKDYHWKHQXPEHUV
WKURXJK
(DFKURZFROXPQDQGER[PXVWKDYHWKHQXPEHUV
WKURXJK
&LUFOHZRUGVWRWKH5,*+7RU'2:1(YHU\OHWWHULVXVHGH[DFWO\21&(
+ 3 $ 5 $ ' 2 ; , & $ / , ( ( ; $ 0 , 1 $ 7 , 2 1 6 1 7
* 7 - 7 2 3 $ / ( 7 7 ( 6 7 : 5 2 2 1 2 6 ( 0 8 ' 7 2 ( ( ,
, : % 7 : 2 6 7 2 0 $ & + 1 &
( 2 0 , 6 ) 2 5 7 8 1 ( 6 ' ( 9 5 6 ( ( $ / 7 , 0 ( 7 ( 5 6 ( ' / 2 $ ) ) 2 8 1 7 $ , 1 6 :ULWHWKHZRUGVIRXQG
)2817$,16 $/7,0(7(56
&LUFOHZRUGVWRWKH5,*+7RU'2:1(YHU\OHWWHULVXVHGH[DFWO\21&(
$ 6 & 2 1 6 , ' ( 5 $ % / ( ) , 1 7 ( 5 9 ( 1 ( $ * ( 1 7 (
$ 1 $ 7 ( $ 6 3 , 5 $ 1 7 6 ' / + 2 $ ; ( 6 3 $ 5 5 2 7 6 )
< = 2 2 0 ( 7 + 2 ' , & $ / , 5 3 ( $ 5 & ( , / , 1 * 6 / , 7 5 , ) / ( 6 5 2 ' ( 1 7 (
& + 8 * ) ( ' ( 5 $ 7 , 2 1 6 :ULWHWKHZRUGVIRXQG
)('(5$7,216 ),/(
6HOHFWWKHZRUGRUSKUDVHZKRVHPHDQLQJLVFORVHVWWRWKHJLYHQZRUG
&29(7
VSXUQ IRUHFDVW UHWDLQ FRS\
UHOLVK
%8&2/,&
XUEDQ FRPSOHPHQWDU\
SRSXODWHG UXVWLF DJHG
(;3(',7(
RXWZHLJK UXQRXW IRUJHW VSHHGXS HMHFW
92/$7,/(
XQVWDEOH VHUHQH LQFLSLHQW WUHPEOLQJ YLFDULRXV
,*1,7(
HYHQLQJSDUW\
FRQVWUXFW VSDUN VQXIIRXW UHOD[
),$6&2
DQQXDOHYHQW SHWIRRG GHEDFOH VXFFHVV PXVLFJHQUH
35,67,1(
VQRZ\
SXUH DUWIXO FUHDWLYH FKLOOHG
%$1,6+
VHWWOH FDVWRXW UHWXUQ DFFUXH FOHDQXS
/85,'
FOHDU UDELG JUDSKLF GUDVWLF VHGXFWLYH
1RZILQGWKHJLYHQZRUGV$1'WKHDQVZHUVLQWKHZRUGVHDUFK,I\RXFDQWILQGDQDQVZHU\RXPLJKWEHZURQJ
5 & ( 7 , 1 * , / , 7 & 1 . 8 $ 1 / 5 , 6 $ % ( 3 1 ( 3 1 ( 6 ( 8 ' 1 8 , $ & 5 5 2 2 ( ' $ & 9 2 / $ 7 , / ( 3 1 ( 8 3 5 7 6 2 2 / $ $ , ) 5 7 ( ; & ; 8 / 6 / 3 ) % 5 5 & & ( , 2 ( % 5 / + + 5 ) 6 ( / , , 5 , , 6 2 7 ( / & 8 1 6 7 $ % / ( ( , 1 ; 7 ( ( , 5 7 ( ( ' ( 2 , 5 ( 2 $ , 8 6 , ( $ $ 6 , 8 & * & / 7 & 3 , $ ( ' 7 $ 7 $ 1 / 8 6 / 6 7 / ' / , 5 9 6 % & $ 6 7 2 8 7 9 & , ( , 7 ( / 8 7 . 6 < ( , $ 7 ( ) , $ 6 & 2 & & ( 7 / $ 2 9 $ & 7 6 % 8 8 2 6 , ( 3 6 % 5 $ ' 6 6 ( 3 ) * ( / 8 5 , ' 3 $ & ( ( & 3 % & + 1 , & % , ' 6 3 $ 5 . / ( +
% $ 1 , 6 + 8 8 8 $ , 8 ( 8 7 2 ( & , / 2 & 8 % 6 5 & % 7 3 $ ( 6 *
$ / 5 $ , ' ( ; 3 ( ' , 7 ( % 2 7 & , + 3 $ 5 * ( 9 3 ( , 5 6 ; $ 8
Start on the B circle. Do not pick up your pencil. Draw a line going left, right, up, or down.
Every line must end on a circle. No stopping on an empty box. Try to collect all the circles and end your last line on the E circle. You can go through a circle more than once.
E
B
Didn't get them all? That's ok. This was hard. I missed only circles.